Novel LKF Method onH∞Synchronization of Switched Time-Delay Systems
研究了切换非线性时滞系统的H∞全局渐近同步问题，通过引入模式依赖的双重事件触发机制节省通信资源，并设计新型多Lyapunov-Krasovskii泛函降低保守性，同时给出线性矩阵不等式形式的同步准则，数值例子和图像处理应用验证了方法的有效性。
This article investigates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> global asymptotic synchronization (GAS) of switched nonlinear systems with delay. By introducing mode-dependent double event-triggering mechanisms (DETMs), the communication resources in both system–controller (S-C) channel and controller–actuator (C-A) channel are saved as much as possible. By designing a new multiple Lyapunov–Krasovskii functional (LKF) with time-varying matrices and developing novel analysis techniques such that the increment of the LKF at switching instant is smaller than one, not only the conservatism of obtained results is greatly reduced but also the nonweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula> -gain is convenient to be derived without using any conservative transformation. The exclusion of the Zeno behavior of the DETMs is proved. Synchronization criteria formulated by linear matrix inequalities (LMIs) are given, by which the control gains, event-triggering weights, as well as the minimum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula> -gain are simultaneously designed. Numerical examples demonstrate the low conservatism of the theoretical analysis. Meanwhile, image processing on the basis of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> GAS is provided to further illustrate the perfect performance.